(x+3)(x+1)(x+2)(x+4)>120
[(x+1)(x+4)][(x+2)(x+3)]>120
[(x^2+5x)+4][(x^2+5x)+6]>120
(x^2+5x)^2+10(x^2+5x)+24-120>0
(x^2+5x)^2+10(x^2+5x)-96>0
(x^2+5x+16)(x^2+5x-6)>0
x^2+5x+16=(x+5/2)^2+39/4>0
所以x^2+5x-6>0
(x+6)(x-1)>0
x>1.x